Through a question from another user, I came across a problem where the client is unable to connect to a service.
If you click on “Use My Teamspeak” nothing happens.
To reproduce the error:
During setup, select a server which you are already hosting yourself and which is displayed in the “Chose your home” list.
After that you get an error message and repeat the chat setup process and this time select “Find Server”, then select “my teamspeak”.
Edit: After restarting the client, everything seems to work.